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Troubles with Indeterminate Symbols (VIDEO)

24 July 2024 / Krystian Karczyński

This post is a kind of response to the question: "I don't understand something and I need an explanation, why do you simplify 'n'? I mean that n/n is an indeterminate symbol (infinity over infinity) help because I'm already lost with this." Understanding what indeterminate symbols REALLY are can be quite tricky. It also raises many questions about what you "can" and "can't" do with them.

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A Few Things You Should Learn Well in High School, But No One Told You – Part 4: The Square Root of x Squared

22 July 2024 / Krystian Karczyński

Today, it's going to be short. My quick question for you is: What is the square root of x squared? When I was still giving tutoring sessions, I asked this question to many high school and college students. Do you know how many knew the correct answer? Two.

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A Few Things You Should Learn Well in High School, But No One Told You – Part 3: Quadratic Function

22 July 2024 / Krystian Karczyński

This post is already the third in a row where I want to draw your attention to things that are worth reviewing at the very beginning of your mathematics studies at university. A quick review of them will make your life in university much easier. Today it's the turn of the quadratic function. Quadratic function? The topic of the quadratic function is, of course, very broad, and I don't mean at all that you should take a high school textbook and go through the entire chapter from cover to cover. Let's just focus on a few important details, nuances, and traps.

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A Few Things You Should Have Learned Well in Middle School, But No One Told You – Part 2: Quantifiers

16 July 2024 / Krystian Karczyński

Quantifiers - but they weren't really there... Alright, but who needs this? In most mathematical definitions and theorems, concepts like "every" and "exists" are used. See how to use them correctly.

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A Few Things You Should Learn Well in High School But No One Told You – Part 1 Absolute Values

15 July 2024 / Krystian Karczyński

If you’ve been studying mathematics at university for a while now, you’ve probably noticed that most of the material covered in high school doesn’t directly help you at university. If you’re just starting out - take note of this. Let’s get to work. In this and the next posts, I’ll show you a few details, understanding which will greatly ease your university studies. We start with... The geometric interpretation of absolute value (as distance).

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High school graduates ask, eTrapez answers. Derivation of the height formula in a right-angled triangle.

09 July 2024 / Krystian Karczyński

This post is dedicated to a piece of a high school exam question sent to me by a high school graduate via email. It's worth taking a look out of curiosity and never repeating again that university math is harder than advanced high school math. Here I show the derivation of the height formula in a right-angled triangle.

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The Symbol 0 in the Limits of Functions and Sequences

27 June 2024 / Krystian Karczyński

When working with limits of functions and sequences, we frequently come across various mathematical oddities, such as: 0/0 or 1/0. The question is - what do they mean? I often come across completely incorrect opinions like: "at higher levels in mathematics, you can divide by 0".

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Some Things You Should Have Learned Well in High School But Nobody Told You So – Part 5 Multiplying or dividing inequalities on both sides

18 October 2011 / Krystian Karczyński

In this post, I will continue with topics from high school that you may not have placed much emphasis on, but which will make your life much easier when you go to college. This is part 5 - if you just came here now, you can take a look at the previous 4 posts :) Here I will deal with mutual multiplication and division of inequalities.

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Calculator for the area

21 February 2014 / Krystian Karczyński

I present another of “my” calculators, this time determining the domain of a function:

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